Volume of Rectangular Prisms

5th Grade MathMeasurement and Data4 pages

About this worksheet

Volume of rectangular prisms for 5th grade math, moving from cube-counting to formulas (Common Core 5.MD.5.a and 5.MD.5.b). Two cube-built diagrams open the sheet, where students find the base layer, count the layers, and multiply: 4 by 3 by 2 gives 24 cm³. Formula problems follow, including a shipping carton at 8 × 5 × 6 = 240 cubic inches and two prisms defined by base area and height. Real-world questions fill a planter with 36 cubic feet of soil, part-fill a classroom fish tank to a 9-inch water line, and compare two storage bins that both come out at exactly 240 cm³.

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$Volume of Rectangular Prisms: Measurement and Data - page 1$

$Volume of Rectangular Prisms: Measurement and Data - page 2$

$Volume of Rectangular Prisms: Measurement and Data - page 3$

$Volume of Rectangular Prisms: Measurement and Data - page 4$

Curriculum objectives covered

5.MD.5.a

“Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.”

Part 1's two diagrams pack prisms with unit cubes and show the count matching base layer times layers, 12 × 2 and 10 × 4.

5.MD.5.b

“Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.”

Parts 2 and 3 apply both formulas: V = l × w × h for the carton, container, planter and tank, and V = B × h for questions 5, 6 and Bin B.

What's inside this worksheet

Part 1: Layers and Unit Cubes

For two cube diagrams (4 × 3 × 2 and 5 × 2 × 4), students record the base layer, the number of layers, and the total: 24 cm³ and 40 cm³.

Part 2: Calculate the Volume

Four prisms get computed: a shipping carton at 8 × 5 × 6 = 240 in³, a storage container at 12 × 4 × 3 = 144 ft³, and two problems given as base area times height, 35 × 2 and 48 × 5.

Part 3: Real-World Problem Solving

Maya's planter takes 6 × 3 × 2 = 36 cubic feet of soil. A 20 by 10 by 12 inch fish tank holds 2,400 in³ full but only 1,800 in³ at a 9-inch water height. Question 9 compares Bin A (10 × 6 × 4) with Bin B (base 30 cm², height 8 cm) and finds them equal at 240 cm³.

Answer key

Each answer shows the multiplication chain, such as 8 × 5 × 6 = 40 × 6 = 240, so students can see exactly where their own arithmetic went wrong.

How teachers use it

Bridging cubes to formulas

Part 1 is the bridge lesson on a page. Insist students write the layer sentence (8 cubes × 3 layers) before allowing the bare formula, or the h in V = B × h stays meaningless.

The part-filled tank

Question 8b is the thinker: the tank is 12 inches tall but the water stops at 9. Students who reuse 12 have applied the formula without reading, which is worth naming aloud.

Formula-equivalence debate

Question 9 stages V = l × w × h against V = B × h and they tie at 240 cm³. Ask the class whether that tie is a coincidence, and let the argument surface the associative property.

More 5th Grade Math worksheets

Operations with Fractions Place Value and Decimals Geometry Order of Operations

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